9. At the door or inside — distance from the edge · Dr. Seok's Tumour-Infiltrating Lymphocytes, First Steps

Pathology reports contain phrases like "lymphocytes arranged as a band at the tumour periphery" and "infiltrating into the tumour parenchyma".

The first describes immune cells that reached the door but could not get in; the second, ones that got inside. The one linked to checkpoint-inhibitor response is mostly the second.

The infiltration rate cannot separate them. But the map still holds that information.

One cell is 50 µm, so a depth of 20 cells is 1 mm in from the edge.

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import til
from scipy import ndimage

c = til.tilmap("TCGA-BR-8483")
depth = ndimage.distance_transform_edt(c >= 1)     # distance to the edge per tissue cell

lympho = depth[c == 2]
tissue = depth[c >= 1]
print("mean depth of all tissue     %6.2f cells" % tissue.mean())
print("mean depth of lymphocytes    %6.2f cells" % lympho.mean())
print("ratio                        %6.2f" % (lympho.mean()/tissue.mean()))
print()
print("Above 1 means the lymphocytes sit deeper than the tissue average.")

Compare a slide whose lymphocytes stayed at the edge with one where they went deep.

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In most cancer types the ratio hovers near 1 — lymphocytes sit at about the same depth as the tissue.

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import til

d = til.slides()
d = d[(d.til_patches > 200) & (d.depth_tissue > 0)].copy()
d["ratio"] = d.depth_til / d.depth_tissue

print("overall median %.3f" % d.ratio.median())
print("%.1f%% of slides are above 1" % (100*(d.ratio > 1).mean()))
print()
t = d.groupby("tumor").ratio.agg(slides="count", median="median").round(3)
t = t[t.slides >= 30].sort_values("median", ascending=False)
t["cancer"] = [til.NAMES_EN[x] for x in t.index]
print(t.to_string())

Read the result honestly. The median ratio is 1.05 and 60% of slides are above 1. The spread across cancer types is small too, from 1.13 (cervix) to 0.98 (pancreas).

Less dramatic than you hoped. Why?

This map has no tumour boundary. We measured against the "tissue edge" (the border with the glass), not the tumour margin, so it is not the thing pathology means.
A whole slide is cut into many fragments, so there is a great deal of edge.

Even so, on individual slides the difference is stark. Look at the two maps in the widget — 0.48 against 2.20. A signal that vanishes in a group average but survives at the individual level: also a common thing.

🤔 Check yourself

What is the fundamental limitation of measuring depth this way in this data?

🤔 Check yourself

Why not test a freshly invented metric against survival straight away?